@Zhaph-BenDuguid: I took the other question to be about the nature of the LEGO (mostly unsorted sets), whereas this one is more about good places to sell. For this reason, I don't think they're quite the same question, even though they are related. If we need to discuss this further, I suggest we take it to meta.
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KramiiAug 13 '14 at 15:20

Some people still rely on newspaper etc. adds for their purchases. Although they reach a smaller audience, they have three advantages over eBay:

Ads are generally a fixed price, so fees don't depend on selling price - ideal for large lots of LEGO.

If you sell locally, you don't have to charge postage, as buyers can generally collect.

It is arguable that people who mainly buy from local adds are generally less well informed about "realistic" prices than people who use web-based purchasing options, so may be willing to pay a little more (although this cuts both ways - they may under-estimate the true price of things, too).

eBay

Despite your aversion to eBay, it is still be your best bet, simply because you'll reach such a large market. Prices on eBay are driven by the market - by what people are willing to pay. For this reason, I'm not sure that it makes sense to say that it is "too cheap".

To get the best price for your LEGO, I suggest using the fixed price listing feature, setting the price at the lowest you're willing to accept. Of course, it may take a little longer to shift your collection if your prices are at the high end of what the market can tolerate. An excellent picture and a good description make a big difference, too, as can your willingness to ship overseas. If you do decide to ship internationally, don't make the mistake of underestimating postage costs.

I use eBay for all my LEGO sales, and I'm generally happy with the results. The only down-side is that the fees can be quite high, but I generally accept that for the convenience.

Is the set new in the box, and never opened? Is it retired and rare? In that case, the skies the limit since the set may not be available anywhere. When I find my self in this situation I generally list for the high-end price on brickpicker, but include a best offer option.

Do you have the manual, the box it came in and all of the parts and minifigures? Then head on over to brickpicker.com and look up the trending used prices on the sets you want to sell. Use this information to sell the item on ebay (but be ready to pay Ebay 15% of your sale price right off the bat!). You can also try to sell locally, but you will have a hard time finding anyone willing to pay your asking price for what they will consider old used lego.

Is the set complete, but you have no box? See above, but adjust your asking price.

Are we talking about a collection from your childhood that is in a tub in your parents garage? An unsorted lot? A bunch of 'sets' of undetermined completeness? Aim for $10 per pound, but accept $5 cause it sounds like you may be in a hurry.